IGCSE Mathematics - Additional (0606) — May–June 2025, Paper 21
11 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →A curve has equation y = x^2 + 2x − 3. Use the method of completing the square to find the coordinates of the stationary point on the curve.
Answer this question and get it marked →In this question, k is a constant. It is given that 2x^2 + (3k − 2)x + k = 0 has roots that are real and distinct. Find the set of possible values of k.
Answer this question and get it marked →A sports club has the following members: 5 runners, 4 swimmers, 3 gymnasts. These members stand in a straight line. Find the number of ways that this can be done when all the…
Answer this question and get it marked →The coordinates of points A, B, C and D are as follows. A(−4, 3) B(6, −9) C(15, 10) D(14, −1) The line L has equation y = 11x − 75. The perpendicular bisector of the line AB meets…
Answer this question and get it marked →Given that y = x^2 tan(x/2), use calculus to find the approximate change in y as x increases from π/3 to π/3 + h, where h is small.
Answer this question and get it marked →Using an appropriate quadratic factorisation, find the first three terms in the binomial expansion of (9x^2 + 12x + 4)^5, in ascending powers of x. You must simplify your…
Answer this question and get it marked →The function f is defined by f(x) = 2e^(−x) + 3 for x ∈ ℝ. On the axes, sketch the graph of y = f(x) and hence, on the same axes, sketch the graph of y = f^(−1)(x). Show clearly:…
Answer this question and get it marked →Solve the equation (2 − 3 cot x) cos x = 0 for 0 < x ⩽ π/2.
Answer this question and get it marked →In this question, all lengths are in centimetres and all angles are in radians. The diagram shows a sector AOB of a circle, centre O, radius 15. Angle AOB = 6π/5. The sector is…
Answer this question and get it marked →A particle P moves in a straight line. t seconds after passing a fixed point, O, the acceleration of P, a m s^(−2), is given by a = t^2 − 2 for 0 ⩽ t ⩽ 4 a = 19 − 5e^(8 − 2t) for…
Answer this question and get it marked →A geometric progression has first term a and common ratio r, where r 0. The sum of the 2nd and 3rd terms of the progression is 168. The sum of the 4th and 5th terms of the…
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